A vector $\overrightarrow{\mathrm{A}}$ when added to the sum of the vectors $(\hat{\imath}-2 \hat{\jmath}+2…
A vector $\overrightarrow{\mathrm{A}}$ when added to the sum of the vectors $(\hat{\imath}-2 \hat{\jmath}+2 \hat{k})$ and $(-2 \hat{\imath}+\hat{\jmath}-\hat{k})$ gives a unit vector along $\mathrm{y}$ -axis. The magnitude of the vector $\overrightarrow{\mathrm{A}}$ is
$\sqrt{3}$
$\sqrt{6}$
$\sqrt{8}$
$\sqrt{10}$
Solution
$\vec{A}+(\hat{\imath}-2 \hat{\jmath}+2 \hat{k})+(-2 \hat{\imath}+\hat{\jmath}-\hat{k})=\frac{\hat{j}}{\begin{array}{l}\text { unit } \\ \text { vector along Y axis }\end{array}}$
$\vec{A}=\hat{\imath}+2 \hat{\jmath}-\hat{k}$
$|\vec{A}|=\sqrt{6}$